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Vertices Of Self-Similar Tiles, Da-Wen Deng, Sze-Man Ngai

Department of Mathematical Sciences Faculty Publications

The set V_n of n-vertices of a tile T in \R^d is the common intersection of T with at least n of its neighbors in a tiling determined by T. Motivated by the recent interest in the topological structure as well as the associated canonical number systems of self-similar tiles, we study the structure of V_n for general and strictly self-similar tiles. We show that if T is a general self-similar tile in \R² whose interior consists of finitely many components, then any tile in any self-similar tiling generated by T has a finite …